Spectroscopic devices are commonly used to non-invasively measure a characteristic of biological tissue. Spectroscopic devices emit light into biological tissue and detect differences in light absorption to determine the concentration of certain constituents in the biological tissue (e.g., oxygen, hemoglobin, melanin, etc.). The performance of a spectroscopic device is dependent upon its ability to generate sufficient optical power to penetrate the biological tissue of interest and to distinguish against confounding noise (e.g., caused by background light or electrical interference within the environment). Signal-to-noise considerations favor maximizing the optical power of the light emitted into the biological tissue. However, problems can arise when spectroscopic devices output high optical power light for extended periods of time or at fast repetition rates. For example, under certain operation conditions, spectroscopic devices may become undesirably hot. To avoid such problems, spectroscopic devices may be configured to output high optical power light for only short, sequential durations of time. Such spectroscopic devices detect light signals over short, sequential durations of time. The short duration of the detected light signals can make it difficult to use aggressive filtering techniques to remove confounding noise from the detected light signals; e.g., aggressive filtering techniques may add distortion to short duration detected light signals. Aspects of the present invention are directed to systems and methods for spectroscopic measurement of a characteristic of biological tissue which involve output of light having high optical power, short duration, and/or fast repetition rate, which prevent a spectroscopic device from becoming undesirably hot, which involve filtering detected light signals to remove confounding noise, and which account for distortion added to detected light signals during filtering.